A work team of four people completes half a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people.)
I just would like a bit help.
10/4 as many people, so 4/10 the time
15 * 4/10 = 6 days
Idk
To solve this problem step-by-step, let's first find out how many days it takes the initial team of four people to complete the entire job.
Since the team of four people completes half the job in 15 days, it means they complete one-fourth (1/2 รท 2) of the job in 15 days. Therefore, it takes them 15 days to complete one-fourth of the job.
Now, we can calculate the total number of days it takes that team to complete the whole job by multiplying the number of days it takes them to complete one-fourth of the job by 4 (since they are four people).
15 days * 4 people = 60 days
So, the initial team of four people takes 60 days to complete the entire job.
Next, let's calculate how long it will take the team of ten people to complete the remaining half of the job.
Since the initial team of four people completed half the job in 60 days, it means they completed one-half (the remaining half) of the job in 60 days. So, now we need to find out how long it will take the team of ten people to complete one-half of the job in terms of days.
Let's assume that each person in both teams works at the same rate. Therefore, we can say that 10 people working together can complete the job in 60/x days.
Since the initial team completed one-half of the job in 60 days, it means they completed the remaining half of the job in another 60 days. Therefore, we can set up the following equation:
10 people * (60/x days) = 60 days
Solving this equation will give us the value of x, which represents the number of days it will take the team of ten people to complete the remaining half of the job.
10 * 60/x = 60
Dividing both sides by 10:
60/x = 6
Cross-multiplying:
60 = 6x
Dividing both sides by 6:
10 = x
So, it will take the team of ten people 10 days to complete the remaining half of the job.
Therefore, a team of ten people will take 10 days to complete the remaining half of the job.
Sure! Let's break down the problem step by step to find the solution.
Step 1: Calculate the work rate of the four-person team.
If the team of four people completes half the job in 15 days, it means that each day they complete 1/30th of the job (since half the job is completed in 15 days).
Step 2: Calculate the work rate of a single person.
Since the team of four people works at the same rate, the work rate of each person will be 1/30th divided by 4, which is 1/120th of the job per day.
Step 3: Calculate the time required for a single person to complete the remaining half of the job.
Since each person completes 1/120th of the job in a day, to complete the remaining half of the job, they will need to work for 1/60th of the job.
Step 4: Calculate the number of days required for ten people to complete the remaining half of the job.
Since each person completes 1/120th of the job per day, ten people working together will complete 10 times that amount. Therefore, it will take ten people working together 1/12th of a day to complete the remaining half of the job.
So, to sum it up, a team of ten people will take (1/12)th of a day to complete the remaining half of the job.